First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method

under review
  • In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Ambros GleixnerORCiD, Nils-Christian KempkeORCiD, Thorsten KochORCiD, Daniel RehfeldtORCiD, Svenja Uslu
Document Type:In Proceedings
Parent Title (English):Operations Research Proceedings
Tag:block structure; energy system models; high performance computing; interior-point method; linear programming; parallelization; preprocessing; presolving
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C05 Linear programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C06 Large-scale problems
Year of first publication:2019
Preprint:urn:nbn:de:0297-zib-74084